Coupled order parameters, symmetry-breaking irrelevant scaling fields, and tetracritical points

The phase diagrams of systems described by a Hamiltonian containing an anisotropic quadratic term of the form 12g=1^nc_{x}^S_^2 (x), and a cubic anisotropic term =1^n{x}^S_^4 (x), are studied using mean-field theory, scaling theory, and expansions in (=4-d) and 1n. Here, S_ (x) (a=1, , n) is a local n-component ordering variable. Systems to which the analysis is applicable include perovskite crystals, stressed along the 100 direction (n=3), anisotropic antiferromagnets in a uniform field, uniaxially anisotropic ferromagnets, ferroelectric ferromagnets and crystalline ^4He (n=2). When g=0 and T=T₂ these systems undergo a phase transition that may be associated (for small n) with the Heisenberg fixed point (^*=0) or (otherwise) with the cubic fixed point (^*>0) of the renormalization group. Although is an "irrelevant variable" in the former case, it is found to have important effects. For 0, the "flop" line splits into two critical lines, associated with transitions between each of the ordered phases and a new intermediate phase; the point T=T₂, g=0 is then tetracritical. The shape of the boundary of the intermediate phase is given by T=T₂ (g, ) with T₂-T₂ (g, ) (g{) }^1{{₂}}, where ₂=₆-_ (if the tetracritical point is Heisenberg-like) or ₂=₆^C (if it is cubic). Here, ₆, _, and ₆^C are appropriate crossover exponents associated with the two symmetry-breaking perturbations. The phase diagram of 111 -stressed perovskites is also discussed and the experimental situation briefly reviewed.